Circle Corner

• Circle corner (a two-dimensional figure) is a right triangle having acute vertices on a circle with the hypotenuse outside the circle.
• Chord is a line segment on the interior of a circle.
• Segment of a circle is an interior part of a circle bound by a chord and an arc.

 

area of a Circle Corner formula

\(\large{ A_{area} = \frac{a\;b \;-\; r \; l \;+\; s \; \left(r \;-\; h\right)  }{2 }   }\)

Where:

Units	English	SI
\(\large{ A_{area} }\) = area	\(\large{ft^2}\)	\(\large{m^2}\)
\(\large{ l }\) = arc length	\(\large{ft}\)	\(\large{m}\)
\(\large{ s }\) = chord length	\(\large{ft}\)	\(\large{m}\)
\(\large{ a, b }\) = edge	\(\large{ft}\)	\(\large{m}\)
\(\large{ r }\) = radius	\(\large{ft}\)	\(\large{m}\)
\(\large{ h }\) = segment height	\(\large{ft}\)	\(\large{m}\)

 

Arc Length of a Circle Corner formula

\(\large{ l =  r \; \theta  }\)

Where:

Units	English	SI
\(\large{ l }\) = arc length	\(\large{ft}\)	\(\large{m}\)
\(\large{ \theta }\) = angle	\(\large{deg}\)	\(\large{rad}\)
\(\large{ r }\) = radius	\(\large{ft}\)	\(\large{m}\)

 

Chord Length of a Circle Corner formula

\(\large{ s = a^2 \; b^2   }\)

Where:

Units	English	SI
\(\large{ s }\) = chord length	\(\large{ft}\)	\(\large{m}\)
\(\large{ a, b }\) = edge	\(\large{ft}\)	\(\large{m}\)

 

Height of a Circle Corner formula

\(\large{ h = r \; \left( 1 - cos \; \frac{\theta}{2} \right)    }\)

Where:

Units	English	SI
\(\large{ h }\) = segment height	\(\large{ft}\)	\(\large{m}\)
\(\large{ \theta }\) = segment angle	\(\large{deg}\)	\(\large{rad}\)
\(\large{ r }\) = radius	\(\large{ft}\)	\(\large{m}\)

 

Perimeter of a Circle Corner formula

\(\large{ p = a + b + l   }\)

Where:

Units	English	SI
\(\large{ p }\) = perimeter	\(\large{ft}\)	\(\large{m}\)
\(\large{ l }\) = arc length	\(\large{ft}\)	\(\large{m}\)
\(\large{ a, b }\) = edge	\(\large{ft}\)	\(\large{m}\)

 

Segment Angle of a Circle Corner formula

\(\large{ \theta =   arccos \;  \frac{ 2\;r^2 \;-\; s^2 }{2\;r^2}  }\)

Where:

Units	English	SI
\(\large{ \theta }\) = segment angle	\(\large{deg}\)	\(\large{rad}\)
\(\large{ s }\) = chord length	\(\large{ft}\)	\(\large{m}\)
\(\large{ r }\) = radius	\(\large{ft}\)	\(\large{m}\)